Formation of closein terrestrial planets disk inner boundary

Formation of close-in terrestrial planets: disk inner boundary, disk-planet interactions and giant impacts Shigeru Ida (Tokyo Tech) collaborators: Masahiro Ogihara (Tokyo Tech), Doug Lin (UCSC) p p p formation of non-resonant, multiple close-in super- Earths (which exist around 40 -60% (? ) of solar type stars) N-body simulation (Ogihara & Ida 2009, Ap. J) • disk inner edge -- cavity or not ; stacked or penetrate 　　　　　　　 planet trap due to e-damping? population synthesis model (Ida & Lin, in prep. ) • type-I migration -- Tanaka et al. (2002) or Paardekooper et al. (2009) • resonant trapping & giant impacts INI, Cambridge, Oct 23, 2009

Motivation: RV observation of super-Earths p p ~40 -60%(? ) of FGK dwarfs have short-P (~0. 1 AU) super-Earths without signs of gas giants ~80%(? ) of the super-Earth systems are non-resonant, multiple systems p p Why so common? Why no short-P planet in Solar system? Why not becoming jupiters? Why a~0. 1 AU (> HJs’ a) ? Why non-resonant? ( Terquem & Papaloizou 2007) p Why multiple?

N-body simulation (3 D) Ogihara & Ida (2009, Ap. J 699, 824) Sg type-I mig & e-damp: Tanaka et al. 2002 Tanaka & Ward 2004 resonantly trapped stable even after gas depletion Terquem & Papaloizou 2007

N-body simulation (3 D) Ogihara & Ida (2009, Ap. J 699, 824) slower mig adiabatic get stacked at the edge Why? detailed analysis

N-body simulation (3 D) Ogihara & Ida (2009, Ap. J 699, 824) slower mig adiabatic instability after gas depletion non-resonant multiple planets at relatively large a population synthesis calculation get stacked at the edge

Semi-analytical calculation of Accretion & migration of solid planets t [yr] M [M ] e 108 107 106 105 giant impacts resonant trapping 0. 1 disk edge disk gas type-I migration (0. 1 x Tanaka et al. ) a [AU] 1 10

Modeling of giant impacts 2 a [AU] 2 1. 5 1 0. 5 0 107 2 x 107 3 x 107 t [yr] Monte Carlo Model - Ida & Lin (2009) : 0 2 x 107 N-body : 6 x 107 t [yr] 108 - Kokubo, Kominami, Ida (2006)

Semi-analytical calculation of Accretion & migration of Solid planets • 2 x. MMSN case • rigid wall edge t [yr] M [M ] e non-res. multiple super-Earths (~0. 1 AU, missed gas accretion) 108 107 106 105 giant impacts resonant trapping 0. 1 disk edge too small to start gas accretion disk gas type-I migration (0. 1 x Tanaka et al. ) a [AU] 1 10

Population Synthesis ~30% Min. Mass Solar Nebula Solar-type stars • various mass disks x 0. 1 x 10 log normal 0. 1 1 Sg 10 (1000 systems) • rigid wall edge

Disk inner cavity ? strong magnetic coupling weak magnetic coupling Cavity No Cavity number of stars channel flow corotation radius Is this picture still valid? 0 Herbst & Mundt 2005 5 10 15 spin period [day]

N-body simulation (3 D) Ogihara & Ida (2009, Ap. J 699, 824) slower mig adiabatic get stacked at the edge Why? detailed analysis

Why stacking at the edge ? 1 M 1 1 M 2 toy model torque on torqueon on body 2 body 11 disk edge *) Martin got the same result e-damping type-I mig planet-planet int. 1 2

Planet trap due to e-damping Vgas(~VK) Tidal e-damping (+ resonant e-excitation) outward migration ! type-I migraion torque: changes sign near cavity modulated by Sg-grad (Masset et al. 2006) e-damping torque: not affected by Sg-grad? Tanaka & Ward formula is OK in this case?

Condition for stacking te/ta = 0. 003 Dredge/redge = 0. 01 te/ta = 0. 003 Dredge/redge = 0. 05 Both te/ta & Dredge/redge must be small for stacking. te / ta ~ ( H / r ) 2 Dredge/redge~ (H/r) ? (H/r) r 1/4 te/ta = 0. 03 Dredge/redge = 0. 01 likely to be satisfied at the disk inner edge 　

Planet formation model (core accretion) Ida & Lin (2004 a, b, 2005, 2008 a, b) start from planetesimals combine following processes planetesimal accretion type-I & II migrations gas accretion onto cores dynamical interactions between planets (resonant trapping, giant impacts) – Ida&Lin(in prep) 　semi-analytical formulae based on N-body & fluid dynamical simulations

Modeling of giant impacts 2 a [AU] 2 1. 5 1 0. 5 0 107 2 x 107 3 x 107 t [yr] Monte Carlo Model - Ida & Lin (2009) : 0 2 x 107 N-body : 6 x 107 t [yr] 108 - Kokubo, Kominami, Ida (2006)

M [M ] Monte Carlo model of giant impacts [close scattering & accretion of rocky embryos] final largest bodies 20 runs each 10 x. MMSN N-body Kokubo et al. (2006) MMSN Monte Carlo 0. 1 x. MMSN eccentricity semimajor axis [AU]

M [M ] Monte Carlo model of giant impacts [scattering & accretion of rocky embryos] final largest bodies 20 runs each 10 x. MMSN N-body Kokubo et al. (2006) MMSN Monte Carlo 0. 1 x. MMSN eccentricity N-body : - Kokubo, Kominami, Ida (2006) - CPU time ~ a few days / run Monte Carlo : - Ida & Lin (2009) - CPU time < 0. 1 sec / run semimajor axis [AU]

Accretion & migration of planetesimals [Gas accretion onto cores is neglected in this particular set of simulation] • 2 x. MMSN case • No gas giant • rigid wall edge • type-I mig: Tanaka et al. ’s speed x 0. 1 t [yr] M [M ] e 108 107 106 105 giant impacts resonant trapping 0. 1 disk edge disk gas type-I migration a [AU] 1 10 CPU time: a few sec. on a PC

Formation of dust-debris disks inner regions: giant impacts – common p outer regions: 1 planetesimals remain DF is strong 6 10 yrs unless gas giants form -2 8 yrs 10 10 debris disks: commonly produced -4 10 p weak [Fe/H]-dependence 1 10 continuous collisions p anti-correlated stochastic collisions of planetesimals of embryos with jupiters? stirred by embryos S/SMMSN p 0. 1 a [AU] 1 10

No-cavity case • 2 x. MMSN case • type-I mig: Tanaka et al. ’s speed x 0. 1 t [yr] M [M ] e 108 107 106 105 giant impacts disk gas type-I migration 0. 1 a [AU] 1 no disk edge 10

Effect of entropy gradient Paardekooper et al. 2009 e M [M ] • type-I mig: Tanaka’s torque is connected to Paardekooper’s at ~10 e-t/tdep. AU t [yr] 108 107 106 105 Tanaka disk gas Paardekooper 0. 1 disk edge a [AU] 1 10

e M [M ] averaged over 20 runs (mean values, dispersion) blue: 3 x. MMSN right blue: MMSN red: 1/3 x. MMSN cavity Tanaka’s torque 0. 1 1 10 a [AU]

p Theoretical predictions ü a ~ 0. 1 AU M [M ] Non-resonant, multiple, short-P Earths/super-Earths ( > disk inner edge = 0. 04 AU) rely on stacking (rigid wall) ü 1 non-resonant, multiple ü ü common indep. of type-I migration rate avoid gas accretion M [M ] (have undergone close scattering & giant impacts) (have grown after disk gas depletion via giant impacts) observation 10 a [AU]

Diversity of short-P terrestrial planets cavity M [M ] no cavity 0. 1 1 10 a [AU] Solar system 0. 1 1 10 a [AU] Short-P super-Earths Saturn satellite system? Jupiter satellite system? Sasaki, Stewart, Ida (submitted)

Population Synthesis ~30% Min. Mass Solar Nebula Solar-type stars • various mass disks x 0. 1 x 10 (1000 systems) • rigid wall edge log normal 0. 1 1 Sg 10

Summary N-body simulations + Synthetic planet formation model including giant impacts & resonant trapping Non-resonant, multiple, short-P Earths/super-Earths p Diversity of close-in planets (Solar system: no close-in planets) diversity of disk inner boundary? p 1) cavity or non-cavity 2) migration trap due to e-damping?